12.3 Spreadsheet Implementation of this Procedure

How can you do such things?
First put
x
and
j
in fixed locations
X
and
Y
.
Then set up the following columns on the spreadsheet:

f(xj)
:

In the first column enter the successive values of
f(xj)
starting with the first, known value.

For roots you can start with
x0=f(x0)=1
.

Compute later values
f(xj)
by using the linear approximation tangent line at
xj−1
evaluated at argument
x,fLxj−1(x)
or
f(xj−1)+f'(xj−1)(x−xj−1)
. (
xj−1
is the entry in the second column in the previous row.)

xj
:

In the second column apply the inverse function,
f−1
to the value in the first column.

Once you have entered your instructions for
f(x1)
and
x1
, you can copy these down a hundred rows, and you are done.